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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Estimates for Green's functions


Authors: A. G. Ramm and Lige Li
Journal: Proc. Amer. Math. Soc. 103 (1988), 875-881
MSC: Primary 35J15; Secondary 35A08
DOI: https://doi.org/10.1090/S0002-9939-1988-0947673-7
MathSciNet review: 947673
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Abstract: Let $ {l_q} = - {\nabla ^2} + q(x),x \in {R^3},0 \leq q \leq c{(1 + \left\vert x \right\vert)^{ - a}},a{\text{ > }}2,{l_q}{G_q}(x,y) = \delta (x - y)$. If $ q \geq p \geq 0,q \not\equiv p$, then \begin{displaymath}\begin{gathered}c\left\vert {x - y\left\vert {^{ - 1}} \right... ...\left\vert {x - y} \right\vert)^{ - 1}},x \ne y \end{gathered} \end{displaymath}, for some positive $ c = c(q)$. If $ p \not\equiv 0$ then $ {G_p}{\text{ < }}{(4\pi \left\vert {x - y} \right\vert)^{ - 1}},x \ne y$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0947673-7
Article copyright: © Copyright 1988 American Mathematical Society

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